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K749

too complicated to be written here. Click on the link to download a text file.

X(1), X(3), X(58), X(500), X(501), X(942), X(3157), X(4303), X(7100)

S = X(1)-Ceva conjugate of X(4303)

A'B'C' : incentral triangle

A"B"C" : cevian triangle of X(4303) in A'B'C'

Q = X(7100) = isogonal conjugate of X(1770) = perspector of ABC and A"B"C"

The extangents triangle TR17 (see TCCT, 6.17) is perspective to :

• the cevian triangle of M for M on K033, the perspector being on K750 = pK(X213, X40),

• the anticevian triangle of M for M on K362, the perspector being also on K750,

• the antipedal triangle of M for M on K749.

K749 is a pivotal cubic with respect to :

• ABC with pivot X(1), isopivot X(4303),

• A'B'C' with pivot X(4303), isopivot S,

• A"B"C" with pivot S, isopivot the (complicated) X(1)-Ceva conjugate of S.

Remark : TR17 is orthologic to the antipedal triangle of any point on the Jerabek hyperbola and parallelogic to the antipedal triangle of any point on the circumconic with perspector X(216) passing through X(110), X(265), X(1625), etc.